For the transmission of digital data over voice grade telephone lines or other band limited channels, data modems are known for encoding data into a form capable of transmission over the limited bandwidth line, and for the decoding of data received over such line. One class of known modems operates at a data rate of 4800 bits per second (bps) and employs differential phase shift keyed (DPSK) modulation using 8 phase modulation of an 1800 Hz carrier. The data bits are processed three at a time to form tribits, each of 8 possible tribit combinations being assigned a corresponding phase angle. One known modem operating at 4800 bps is the Bell System Model 208 in which successive binary tribits are phase shifted from the previous tribit by 45.degree., with a 22.5.degree. offset provided for each of the phase angles; thus, each of the 8 possible tribits is assigned a phase angle starting at 22.5.degree. and progressing at 45.degree. increments to 337.5.degree..